Sharif Digital Repository

The present study aims at the free vibration analysis of double tapered columns. Foundation is assumed to be elastic and the effects of self-weight and tip mass with significant moment of inertia are considered. The governing equation of motion is obtained using the Hamilton principle, based on both the Euler-Bernoulli and Timoshenko beam models. Applying the power series method of Frobenius, the base solutions of the governing equations are obtained in the form of a power series via general recursive relations. Applying the boundary conditions, the natural frequencies of the beam/column are obtained using both models. The obtained results are compared with literature and a very good... 

In this paper, the whirling frequencies of simply supported and clamped rotating cylindrical shells surrounded by an elastic foundation are investigated. The Love's shell theory is used along with the Winkler foundation to obtain the governing equations of motion. An exact power series solution is obtained for arbitrary boundary conditions and the results are verified with the literature. Several case studies are performed, and the effect of spinning speed, foundation stiffness, and geometrical dimensions of the cylinder on the whirling frequencies are investigated  

In this paper the free vibration of single walled carbon nanopeapods encapsulating C60 molecules is considered. The nanopeapod is embedded in an elastic medium and clamped at both ends. The Euler-Bernoulli beam model is used for the carbon nanotube and the C60 molecules are considered as lumped masses attached to the beam. Based on the nonlocal elasticity theory the governing equation of motion is derived and the resonance frequencies of the nanopeapod are obtained. The effects of small scale, foundation stiffness and ratio of the fullerenes' mass to the nanotube's mass on the frequencies are studied and some conclusions are drawn  

The dynamic response of a Timoshenko beam with immovable ends resting on a nonlinear viscoelastic foundation and subjected to motion of a traveling mass moving with a constant velocity is studied. Primarily, the beam's nonlinear governing coupled PDEs of motion for the lateral and longitudinal displacements as well as the beam's cross-sectional rotation are derived using Hamilton's principle. On deriving these nonlinear coupled PDEs the stretching effect of the beam's neutral axis due to the beam's fixed end conditions in conjunction with the von-Karman strain-displacement relations is considered. To obtain the dynamic responses of the beam under the act of a moving mass, derived nonlinear... 

In the present study, free vibrations of single walled carbon nanotubes (SWCNT) on an elastic foundation is investigated by nonlocal theory of elasticity with both beam and shell models. The nonlocal boundary conditions are derived explicitly and effectiveness of nonlocal parameter appearing in nonlocal boundary conditions is studied. Also it is demonstrated that the beam model is comparatively incapable of capturing size effects while shell model captures size effects more precisely. Moreover, the effects of some parameters such as mechanical properties, foundation stiffness, length and radius ratios on the natural frequencies are studied and some conclusions are drawn  

In this paper, a multiplate nonlocal shear model and molecular dynamic simulations are presented to investigate the effects of interlayer shear and nonlocality on the natural frequencies of multilayer graphene sheets (MLGSs). From one aspect in the optimal design of such structures, the interaction between graphene layers, which can significantly vary the static and dynamic behavior due to lack of solidity of layers stack, should be considered. On the other hand, it is requied that the nonlocality phenomenon which has an effective role in the mechanical analysis of nanostructures is taken into account. To this aim, the equation of motion along with corresponding boundary conditions is... 

In this paper, a multiplate nonlocal shear model and molecular dynamic simulations are presented to investigate the effects of interlayer shear and nonlocality on the natural frequencies of multilayer graphene sheets (MLGSs). From one aspect in the optimal design of such structures, the interaction between graphene layers, which can significantly vary the static and dynamic behavior due to lack of solidity of layers stack, should be considered. On the other hand, it is requied that the nonlocality phenomenon which has an effective role in the mechanical analysis of nanostructures is taken into account. To this aim, the equation of motion along with corresponding boundary conditions is...